How to create a Java 8 Stream from an iterator?

static <T> Stream<T> iteratorToFiniteStream(final Iterator<T> iterator) {
    return StreamSupport.stream(Spliterators.spliteratorUnknownSize(iterator, 0), false);
}

static <T> Stream<T> iteratorToInfiniteStream(final Iterator<T> iterator) {
    return Stream.generate(iterator::next);
}